Research on Graph Signal Sampling and Reconstruction Method Based on Causal Emergence

Graph signal sampling and reconstruction techniques effectively reduce data dimensions while preserving the information and structure contained in networks. The distortion-free reduction of data dimensions not only aids in reducing the computational complexity of data but also facilitates the extraction of network features and attributes. This reduction in data dimensions provides convenience for the better analysis and processing of complex network data, ultimately enhancing the efficiency of complex network analysis tasks. Currently, the field of graph signal processing primarily consists of two fundamental frameworks: graph signal processing based on the graph Laplacian matrix and graph signal processing based on the graph's adjacency matrix . Although these two frameworks make full use of the topological structure of graph models, they do not consider the relationships between node information within networks, nor do they integrate individual node information with network structural information. Furthermore, they fail to approach the problem of sampling and reconstruction from the perspective of overall network information. This paper takes the network's intrinsic topological structure and the causal relationships between nodes as its starting point. The goal is to reduce network size and increase the effective information of individual nodes to make the entire network contain richer, valuable information. Combining the graph signal research method based on the graph Laplacian matrix, this paper introduces a graph signal sampling and reconstruction algorithm based on causal emergence. The algorithm initially employs a causal emergence algorithm based on spectral methods to obtain the sampled network and subsequently utilizes classical representation learning algorithms to acquire node representations of the sampled network. This approach enables us to obtain graph signal representations that are richer than those of the original network. Subsequently, we apply a reconstruction framework to reconstruct the obtained graph signals. Finally, the experimental results conducted on three real networks demonstrate that the proposed algorithm outperforms existing theories of graph signal sampling and reconstruction. This research contributes valuable insights and methods to the further development of the field of graph signal processing.